Working out perimeters

Working out perimeters

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using algebraic expressions to find lengths of a shape.
diagram of a shape with side lengths marked

Question 2Change answer

a) Write an expression, in its simplest form, for the length of
i)   side Q: 
ii)  side R: 

Question 2Change answer

b) i) Write an expression that would allow you to find the length of the perimeter around the shape.

Question 2Change answer

ii) Simplify your expression.

Question 2Change answer

c)  Use your expression in b) ii) to find the value of x for a perimater of 104cm.
     Show all your working in your calculation.
Task administration: 
This task is completed with pencil and paper or online.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions
Keywords: 
algebraic expressions, simplify, perimeter, linear equations
Description of task: 
Students evaluate and simplify algebraic expressions for the side lengths and perimeter of a composite shape. They then find x for a given perimeter.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y10 (08/2001)
a) i)
ii)		 x - 1
x - 2		 difficult
difficult
b)
i) 
 Any 1 of (2 marks - difficult):

  • 2(2x - 1) + 2(3x - 2)
  • 3x - 2 + 2x - 1 + x - 2 + x + 2x + x - 1
  • 3x - 2 + 2x - 1 + 2x + x + answer to a) i) + answer to a) ii)
  • Other possible answers.
or
Any 1 of (1 mark - moderate): 
  • 3x - 2 + 2x -- 1 + 2x + x + Q + R
  • 8x - 3 + Q + R
  
b)
ii)
 Any 1 of (1 mark - moderate): 

  • 10x - 6
  • 2(5x - 3)
  • 2(3x - 2) + 2(2x - 1) if not already given in b) i)
  • Answer to b) i) simplified correctly.

NOTE: Give both marks if simplification only is given.

  
c)   Any 1 of (2 marks - very difficult):

  • 11, e.g., working 104 = 10x - 6
    110 = 10x
  • 104 = answer to b) ii) which is then solved correctly.

Correct substitution into b)ii) but incorrect calculation (1 mark - difficult).

  
Diagnostic and formative information: 
 

Common error

Likely calculation

Likely misconception

a) i)
    ii)

(2x - 1) - x
(3x - 2) - 2x

  

Expression not written in its simplest form.

b) i)

2(3x - 2) + 2(2x - 1) - (2x + x)
2(3x - 2 + 2x - 1) - 2(2x + x)

  

Confusion in calculating perimeter with area.

c)

9.8

10x - 6 = 104
\ 10x = 98

Solving equation incorrectly, subtracting instead of adding 6 to the right-hand side.